A high-temperature, gas-cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (k = 57 W/m ∙ K) is encased in graphite (k ≈ 3 W/m ∙ K) and gaseous helium flows through an annular coolant channel. Consider conditions for which the helium temperature is T∞= 600 K and the convection coefficient at the outer surface of the graphite is h = 2000 W/m2 ∙ K.

(a) If thermal energy is uniformly generated in the fuel element at a rate q = 10 8 W/m3, what are the temperatures T1 and T2 at the inner and outer surfaces, respectively, of the fuel element?

(b) Compute and plot the temperature distribution in the composite wall for selected values of q. What is the maximum allowable value of q?

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5 sin 24 = 273 + To, (K) 0<1<12h ) T, o(K) = 273 + 11 sin 24 12